Select The Correct Answer.Simplify: 6 ÷ 3 + 3 2 ⋅ 4 − 2 6 \div 3 + 3^2 \cdot 4 - 2 6 ÷ 3 + 3 2 ⋅ 4 − 2 A. 98 B. 42 C. 36 D. 22

Understanding the Expression

The given expression is $6 \div 3 + 3^2 \cdot 4 - 2$. To simplify this expression, we need to follow the order of operations (PEMDAS):

1. Parentheses: None
2. Exponents: $3^2$
3. Multiplication and Division: $6 \div 3$ and $3^2 \cdot 4$
4. Addition and Subtraction: $6 \div 3 + 3^2 \cdot 4 - 2$

Step 1: Evaluate Exponents

The first step is to evaluate the exponent $3^2$. This means multiplying 3 by itself: $3^2 = 3 \times 3 = 9$.

Step 2: Evaluate Multiplication and Division

Next, we need to evaluate the multiplication and division operations. We have two operations to perform:

1. $6 \div 3 = 2$
2. $3^2 \cdot 4 = 9 \cdot 4 = 36$

Step 3: Evaluate Addition and Subtraction

Now that we have evaluated the multiplication and division operations, we can perform the addition and subtraction operations:

1. $6 \div 3 + 3^2 \cdot 4 = 2 + 36 = 38$
2. $38 - 2 = 36$

Conclusion

The simplified expression is $36$. Therefore, the correct answer is:

C. 36

Explanation

To simplify the expression, we followed the order of operations (PEMDAS). We first evaluated the exponent $3^2$, then the multiplication and division operations, and finally the addition and subtraction operations. By following this order, we arrived at the simplified expression $36$.

Tips and Tricks

• When simplifying expressions, always follow the order of operations (PEMDAS).
• Evaluate exponents first, then multiplication and division, and finally addition and subtraction.
• Use parentheses to group operations and make the expression easier to simplify.

Practice Problems

• Simplify the expression: $12 \div 4 + 2^3 \cdot 5 - 1$
• Simplify the expression: $9 \div 3 + 2^2 \cdot 6 - 4$

Solutions

• $12 \div 4 + 2^3 \cdot 5 - 1 = 3 + 40 - 1 = 42$
• $9 \div 3 + 2^2 \cdot 6 - 4 = 3 + 24 - 4 = 23$

Conclusion

Simplifying expressions is an essential skill in mathematics. By following the order of operations (PEMDAS) and evaluating exponents, multiplication and division, and addition and subtraction in the correct order, we can simplify complex expressions and arrive at the correct answer.

Understanding the Expression

The given expression is $6 \div 3 + 3^2 \cdot 4 - 2$. To simplify this expression, we need to follow the order of operations (PEMDAS).

Q: What is the order of operations (PEMDAS)?

A: The order of operations is a set of rules that tells us which operations to perform first when we have multiple operations in an expression. The acronym PEMDAS stands for:

1. Parentheses: Evaluate expressions inside parentheses first.
2. Exponents: Evaluate any exponential expressions next (e.g., 2^3).
3. Multiplication and Division: Evaluate any multiplication and division operations from left to right.
4. Addition and Subtraction: Finally, evaluate any addition and subtraction operations from left to right.

Q: How do I evaluate exponents?

A: To evaluate an exponent, you need to multiply the base number by itself as many times as the exponent indicates. For example:

• $2^3 = 2 \times 2 \times 2 = 8$
• $3^2 = 3 \times 3 = 9$

Q: How do I evaluate multiplication and division?

A: To evaluate multiplication and division, you need to perform the operations from left to right. For example:

• $6 \div 3 = 2$
• $3^2 \cdot 4 = 9 \cdot 4 = 36$

Q: How do I evaluate addition and subtraction?

A: To evaluate addition and subtraction, you need to perform the operations from left to right. For example:

• $6 \div 3 + 3^2 \cdot 4 = 2 + 36 = 38$
• $38 - 2 = 36$

Q: What is the correct answer for the expression $6 \div 3 + 3^2 \cdot 4 - 2$?

A: The correct answer is C. 36.

Q: What are some tips and tricks for simplifying expressions?

A: Here are some tips and tricks for simplifying expressions:

• Always follow the order of operations (PEMDAS).
• Evaluate exponents first, then multiplication and division, and finally addition and subtraction.
• Use parentheses to group operations and make the expression easier to simplify.

Q: What are some practice problems for simplifying expressions?

A: Here are some practice problems for simplifying expressions:

• Simplify the expression: $12 \div 4 + 2^3 \cdot 5 - 1$
• Simplify the expression: $9 \div 3 + 2^2 \cdot 6 - 4$

Solutions

• $12 \div 4 + 2^3 \cdot 5 - 1 = 3 + 40 - 1 = 42$
• $9 \div 3 + 2^2 \cdot 6 - 4 = 3 + 24 - 4 = 23$

Conclusion

Simplifying expressions is an essential skill in mathematics. By following the order of operations (PEMDAS) and evaluating exponents, multiplication and division, and addition and subtraction in the correct order, we can simplify complex expressions and arrive at the correct answer.